Methods and compound gauge devices for measuring the axial curvature of a tube

ABSTRACT

A number of wall curvature gauges, e.g., two, are mounted independently on a rigid carrier, arrayed equiangularly about the axis of the rigid carrier, to form a compound gauge device. The compound gauge is advanced along the length of a tube, typically through the interior of the tube, with each component gauge generating an electrical signal having a voltage representative of tube wall curvature along the path traced by the respective gauge. The signals are processed concurrently to provide a single continous output voltage signal which is proportional to a weighted algebraic sum of the voltages generated by the individual wall curvature gauges. Where two diametrically opposed wall curvature gauges are employed, the weighted algebraic sum constitutes the difference in signal voltages generated by the two gauges. The single continuous output signal is representative of the pattern of an axial curvature component in a plane along the length of the tube, e.g., the plane defined by two diametrically opposed wall curvature gauges.

United States Patent [191 Gresho METHODS AND COMPOUND GAUGE DEVICES FORMEASURING THE AXIAL CURVATURE OF A TUBE William Milan Gresho, HopewellTownship, Mercer County, NJ.

[75] Inventor:

[73] Assignee: Western Electric Company,

Incorporated, New York, NY.

Filed: Apr. 21, 1972 Appl. No.: 246,210

U.S. C1 33/178 E, 33/174 R Int. Cl.... G0lb 7/28, E2lb 47/08, GOlb 19/26Field of Search 33/174 R, 174 P,

33/174 PA, 178 R, 86,178 E, 178 F, 1 H

References Cited UNITED STATES PATENTS OTHER PUBLICATIONS MillimeterWaveguide and its Accessories, Nov., 1971, Catalogue Tl-7l029-FurukawaElectric Co., Ltd., Tokyo, Japan Dec. 25, 1973 T. Nakahara, M.l-loshikawa, T. Fujiwara, Straightness Deviation of SteelPipe-Waveguide, Sumitomo Elec. Tech. Rev. No. 123-167, p. 57-64 PrimaryExaminer-John W. Huckert Assistant Examiner-Milton S. GersteinAttorney-W. M. Kain et al.

[5 7] ABSTRACT A number of wall curvature gauges, e.g., two, are mountedindependently on a rigid carrier, arrayed equiangularly about the axisof the rigid carrier, to form a compound gauge device. The compoundgauge is advanced along the length of a tube, typically through theinterior of the tube, with each component gauge generating an electricalsignal having a voltage representative of tube wall curvature along thepath traced by the respective gauge. The signals are processedconcurrently to provide a single continous output voltage signal whichis proportional to a weighted algebraic sum of the voltages generated bythe individual wall curvature gauges. Where two diametrically opposedwall curvature gauges are employed, the weighted algebraic sumconstitutes the difference in signal voltages generated by the twogauges. The single continuous output signal is representative of thepattern of an axial curvature component in a plane along the length ofthe tube, e.g., the plane defined by two diametrically opposed wallcurvature gauges.

35 Claims, 7 Drawing Figures METHODS AND COMPOUND GAUGE DEVICES FORMEASURING THE AXIAL CURVATURE OF A TUBE RELATED APPLICATION This patentapplication is closely related to a patent application by W. E. Rapp onCompound Gauge Devices for Measuring the Axial Curvature of a Tube, Ser.No. 246,372, filed on the same data as this application.

BACKGROUND OF THE INVENTION This invention relates to methods andapparatus for measuring the axial curvature of a tube or other elongatedmember and, more particularly, to methods and apparatus for measuringthe axial curvature of a tube or other elongated member by providing asingle, real time indication of the axial curvature. Curvature isdefined mathematically as the rate of change of direction of a paththrough space, in this case the axis of a tube, with respect todisplacement along the path.

In the manufacture of certain tubes, e.g., in forming sections ofwaveguide tubing for use in transmitting millimeter wavelengthcommunication signals, it may be necessary that the axial curvature ofeach section, i.e., the deparature from perfect straightness, beminimal, A minimum radius of curvature of 2,500 feet is typicallydesired for waveguide tubes of approximately 2 inch inner diameter, witha root-mean-square average radius of curvature of at least 5,000 feet.Detailed, accurate measurement of the axial curvature of such tubes is,thus, necessary. Precise axial curvature measurement is, however, aninvolved undertaking, in that curvature ordinarily must be examined at alarge number of points along the axis of a rather long secon of tubing,e.g., 5 or meters long. The curvature examination should preferably becontinuous, i.e., examination along an infinite number of points betweenth ends of each tube.

Measurement of the axial curvature of a tube has previously beenaccomplished by displacing a gauge, in one form or another,longitudinally through the tube being examined. One type of gauge whichhas been utilized consists of an elongated, flexible structure,contacting the inner wall of the tube at a number of locations along thelength of the gauge. A taut wire stretches between forward and rearwardends of the structure to define a straight axis with reference to whichthe radial flexture of a portion of the structure is sensedelectrically.

This type of flexible gauge, while useful in many applications, isconsidered not well suited to provide an extreme degree of accuracy, asrequired in testing sections of millimeter waveguide tubing. For veryprecise measurements to be made with such a gauge, the forward and therearward ends of the wire would both have to be maintained continuouslycentered exactly on the axis of the tube, in spite of curvature in thetube and of any changes in tube diameter, for all longitudinal positionsof the gauge. At the same time, the wire would have to be keptcontinuously taut without affecting the centering of the wire ends.Moreover, the position of the axis of the wire would have to be sensed,at a single known location along the length of the wire, with respect toa contacted point on the inner wall of the tube radially coplanar withthe known location along the length of the wire. Practical problems inachieving these required conditions in this type of flexible gauge, sothat axial curvature may be measured precisely and reliably, areformidable. No such gauge is known to be commercially available.

Another type of gauge has also been employed in attempting to ascertainthe axial curvature pattern of a tube, the gauge providing measurementsof the curvature of an inner wall of a tube undergoing testing. Thiswall curvature gauge (illustrated in FIG. 4 of the drawing) takes theform of a rigid carrier. A radially movable probe contacts the innerwall of the tube between two reference points established bywall-contacting elements at each end of the rigid carrier.

It was initially believed that a single pass of such a wall curvaturegauge through a tube could provide an accurate indication of the axialcurvature of the tube in the plane of the gauge. However, two such axialpasses have since been found necessary to the examination of an axialcurvature component in a plane.

By displacing the rigid carrier twice through the tube at diametricallyopposite positions on the inner wall, wall curvature values may beobtained along two diametrically opposed, longitudinally extending lineson the inner wall. These values may be represented as two traces plottedon a common chart. To determine the axial curvature behavior in theplane defined by the two traces of the gauge through the tube, typicallya horizontal plane, the plotted values of the traces are subtracted onefrom the other at each pair of diametrically opposed points examinedalong the length of the tube. A determination, by subtraction, of thedifference in wall curvature values at diametrically opposite points isnecessary to eliminate non-curvature effects, i.e., effects of tubediameter variations and of gravitational sag. Multiple pairs of opposedlines along the length of the tube may be investigated in like manner.For example, pairs of lines in two mutually perpendicular planes areneeded to provide a complete representation of axial curvature in termsof axial curvature components in the two planes.

This multiple pass method, while accurate and reliable, is burdensome,time consuming and costly, owing to the multiple steps required inanalyzing the data obtained from the gauge so as to yield a meaningfulindication of the axial curvature along the length of a tube ofinterest. Were the wall curvature gauge truly to perform its supposedfunction, a description of the axial curvature behavior in a tube, suchmultiple steps of additional data analysis would not be necessary.Certainly, it does not serve that function.

Clearly, the provision of improved methods and apparatus for measuringthe axial curvature of a tube accurately and reliably in real time in asimple, straightforward manner would be quite advantageous in the art ofmanufacturing certain types of tubes, such as those intended for use inmillimeter waveguide systems.

SUMMARY OF THE INVENTION An object of the invention resides in new andimproved methods and apparatus for measuring the axial curvature of atube or other elongated member.

The invention contemplates the provision of a compound gauge in the formof a single, rigid carrier which supports two or more wall curvaturegauges arrayed equiangularly about the axis of the carrier. The compoundgauge is displaced axially along a tube with the component gauges, iftwo in number, maintained in a common, horizontal plane. Radiallymovable probes on the gauges sense wall curvature values alonglongitudinally extending lines arrayed equiangularly about the axis ofthe tube on a wall surface of the tube, typically the inner wall of thetube. The gauges are supported on the carrier such that each gauge issubstantially independent of the other, except for a correspondence inthe axial locations of the gauges. Thus, the response of each gauge isaffected only by the curvature of the tube wall in the immediatevicinity of the gauge.

A single, continuous electrical signal, having a voltage proportional toa weighted algebraic sum of the wall curvature values sensed by theprobes as the compound gauge is advanced along the tube, is generated.This electrical signal is indicative of the pattern along the length ofthe tube of an axial curvature component in a reference plane definedrelative to the angular po sitions of the gauges. For two gauges, theweighted algebraic sum is a difference between the gauge readings andthe reference plane is the plane of the two gauges. By reorienting thetube with respect to the compound gauge, plural horizontal passes, forexample, in two perpendicular axial planes, may be utilized to providecomplete curvature information by defining the behavior of the curvaturecomponent in each of the planes. With this information, such parametersas the root mean square value, maxima and the periodic content of theaxial curvature over the plural angular orientations may be observed.

BRIEF DESCRIPTION OF THE DRAWING FIG. 1 of the drawing is a plan view,partly in section, of a compound gauge device for measuring the axialcurvature of a tube in accordance with the principles of the invention,illustrating the compound gauge housed within a section of the tube;

FIG. 2 is a side elevational view of the section of the tube and thedevice of FIG. 1, showing additional aspects of the compound gaugedevice;

FIG. 3 is a schematic illustration of an electrical circuit forgenerating a single, continuous voltage signal indicative of the axialcurvature of the tube being measured by the compound gauge;

FIG. 4 is a schematic illustration of a prior art gauge for measuringwall curvature in a tube;

FIG. 5 is a schematic illustration of the individual and combinedeffects of axial curvature, diameter variations and sag on opposed innerwall surfaces of the tube in a horizontal, X-Z plane;

FIG. 6 is a schematic illustration of two spaced radial cross sectionsof a tube, the axial curvature of which is to be measured by a two-gaugedevice such as that shown in FIGS. 1 through 3; and

FIG. 7 is a schematic illustration similar to that of FIG. 6 wheremeasurement is to be made by an alternative, three-gauge device.

DETAILED DESCRIPTION Turning to FIGS. 1 through 3 of the drawing, asection of a tube 11 is illustrated. The tube, while typically of rightcircular cylindrical periphery, may have any shape, e.g., elliptical oreven square, triangular, etc., and may be formed of any suitablematerial, e.g., steel. The tube is to be measured to obtain an accurateand reliable indication of axial curvature as a function of axialposition along the length of the tube.

A compound gauge 12 for measuring axial curvature is shown positionedwithin the tube 1 1. The compound gauge includes a carrier frame, formedby two end members 13 and 14 interconnected by two tie rods 16 and 17.Each end member has a number of springloaded, radially extendingplungers 18,18, which form bearing points for supporting the compoundgauge 12 radially centered within the tube 11.

Two probe carrier bars 19 and 21, constituting the major structuralmembers of two individual wall curvature measuring gauges 22 and 23,respectively, are supported substantially independently in diametricallyopposed positions on the frame. Each bar 19 or 21 is adapted formovement in a radial direction. A pair of springs 24 and 26 force thebars 19 and 21 radially outwardly toward opposite sides of an inner wallsurface 27 of the tube 11.

Two feet 28 and 29 form part of the probe carrier bar 19 or 21 of eachgauge 22 or 23, one foot projecting radially outwardly adjacent to eachend of the bar. A radially outermost tip of each foot 28 or 29 engagesthe inner wall 27 of the tube continuously, under the influence of thesprings 24 and 26 on the bars 19 and 21.

A probe 31 is mounted on each bar in fixed position, e.g., centrally,with respect to the feet 28 and 29 on the bar, and is adapted for radialmovement relative to the bar. The two probes are situated in a commonradial plane, i.e., a plane intersecting the axis of the compound gauge12 perpendicularly. Each probe 31 is coupled mechanically to a differentone of a pair of conventional linear variable differential transformers(LVDTs) 32,32, the LVDTs each being mounted on a different bar 19 or 21.Each LVDT includes an internal biasing spring 33 which maintains aradially outermost tip of the associated probe 31 in continuous contactwith one of a pair of diametrically opposed test points on the innerwall 27 of the tube. The LVDTs provide electrical signals havingvoltages which are indicative of the position of the tip of each probe31 relative to a line between reference points defined by the tips ofthe feet 28 and 29 on the respective probe carrier bar 19 or 21. Acantilever arm 34 supports each probe 31 and LVDT 32 on the respectivecarrier bar 19 or 21 for radial adjustment through manipulation of anadjusting screw 36.

Each of the wall curvature gauges 22 and 23, as described thus far,corresponds generally to a wall curvature gauge 37 known in the priorart, as illustrated schematically in FIG. 4 of the drawing. In order toprovide a better understanding of the present invention,

the functioning of the prior art gauge will now be de scribed withreference to the measurement of a curved wall surface 38 of a tube.

A reference line 39 is defined by the wall-engaging outer tips of twofeet 28' and 29', one adjacent to each end of the wall curvature gauge37. The tip of a probe 31', which may be positioned at any knownlongitudi nal location between the feet 28' and 29, e.g., centrally asshown, engages a test point on the tube wall 38 displaced by a distanceH from the reference line 39. Suitable means, such as an LVDT 32', areutilized to provide an indication of the magnitude of the distance H.

As illustrated in FIG. 4, a circle, having a center C and a radius R,may be defined through the three contact points provided by the gauge,namely the tips of the feet 28' and 29' and of the probe 31 By geometry,the displacement of the probe from the reference line 39, alreadyidentified as the distance H, is directly proportional to the curvaturep of the circle. The curvature is, of course, the inverse of the radiusR. With the probe 31' located centrally of the gauge 37, at a length Lfrom each of the feet 28' and 29, there is established the relationshipSince the distance H is ordinarily quite small in comparison to thedistance L,

R z L /2H Thus, since the length L is known, the indication of thedistance H provided by the gauge 37 constitutes a measure of thecurvature p of the tube wall 38 at the test point engaged by the tip ofthe probe 31' with reference to the points on the wall engaged by thetips of the feet 28' and 29'.

In similar manner, it may be shown that, for any known longitudinallocation of the probe 31' on the gauge 37 intermediate the feet 28 and29' at a spacing s from one of the feet 28' or 29' and with a distance dbetween the feet 28' and 29' p 2H/ds s The foregoing discussionpresupposes that the wavelength of any periodic variation in wallcurvature is longer than the distance between the feet 28' and 29'. Forshorter wavelengths, a correction is necessary, based upon the relativelongitudinal position of the probe 31 with respect to the feet 28' and29'. A gauge 37 of relatively short length is, thus, seen to bedesirable to avoid any need for correction.

The reading provided by the LVDT 32' will now be h considered in moredetail. It was initially assumed that the behavior of the axialcurvature of a tube in a plane would correspond to the behavior of thewall curvature indicated by the LVDT 32' in a single axial pass of thegauge 37 through the tube along such plane. A more complete analysis,however, indicates that the value of the displacement H at any positionalong the tube wall 38 is a function of several factors, such as axialcurvature H,, of the tube (FIG. 5), tube diameter variations H andgravitational sag H in the tube. It will next be demonstrated thatplural passes of the single wall curvature gauge 37 through the tube arenecessary to isolate the indication of axial curvature.

Referring now to FIG. 6, which looks into the tube in the direction ofthe Z axis, it may be seen that, for a component of curvature in oneplane, the X-Z plane in FIG. 6, and no other distortion, a tube crosssection Q will be displaced with respect to a reference cross section Rat a different axial location. In the plane of the displacement, theradial displacement may be observed to be positive, A 71 on one side ofthe cross section Q and negative, A I}, on the other, when measured withrespect to the reference cross section R. It is possible to takeadvantage of this fact through the use of plural passes of the prior;art wall curvature gauge 37 (FIG. 4) through the tube in the manner nextdescribed, the displacement H in FIG. 4 corresponding to the displacement A r, in FIG. 6.

By displacing the wall curvature gauge 37 twice through the tube, with arotation of either the gauge or the tube between the two passes of thegauge through the tube, traces of the value of H may be taken alongdiametrically opposite inner wall surfaces 1 and 2 (FIG. 5) of the tube.The two traces are preferably taken in a horizontal X-Z plane so as toequalize gravitational sag effects on both surfaces. These traces may beplotted on a common chart.

As illustrated at the bottom of FIG. 5, diameter variation and sageffects on the value of A r occur in like radial direction along bothopposed surfaces 1 and 2 in the horizontal plane. Meanwhile axialcurvature effects provide readings of A r which occur in opposite radialdirections for the two surfaces, as discussed previously. Thus, bytaking the value of A r at a test point along surface 1 and subtractingthe value of A r at a test point on diametrically opposed surface 2,i.e., A r A r there may be obtained an indication of the component ofaxial curvature, at the two opposite test points investigated, in theplane of the two points. This indication is substantially free ofdiameter variation and sag effects and, thus, is directly proprotionalto a component of axial curvature in the horizontal plane. Two similarsets of readings in mutually perpendicular planes, providing indicationsof axial curvature components in the two planes, will furnish completeaxial curvature information for tube characterization, as more fully setforth next.

Curvature is a vector function which describes the rate of change in thedirection of an axis with respect to displacement along the axis.Employing mutually perpendicular X-Y-Z coordinates, and with the tubeaxis aligned as closely as possible with the Z axis, the exact locationof the tube axis may be described as a function of z.

The vector location of the tube axis is respect to z and isperpendicular to T(z). The curvature p (z) is p N11) d x(z)/dz 7+ay(z)/dz 7 For the compound gauge 12 of the present invention awn/1Z F=k (A 7*, A 7,

and

m/ 1: 7 MA A a) y where k is a proportionality factor and A and A 7 arethe radial displacements of the tips of the two probes 31,31, as shownin FIG. 6 of the drawing, taken in the X-Z and Y-Z planes in Equations(9a) and (9b), respectively.

It may be observed from Equation (8) that, in a precision tube,curvature has components in the X and Y directions, these componentscorresponding to the second derivatives of X and Y axis coordinates withrespect to 2. Thus, measurement of the curvature of a precision tube inthe two, mutually perpendicular X-Z and Y-Z planes, as defined inEquations (9a) and (9b), yields a complete description of the axialbehavior of the tube.

Returning now to the compound gauge 12 of the present invention, asillustrated in FIGS. 1-3, its operation will next be discussed. Thecompound gauge is located in the tube 11, e.g., adjacent to one end ofthe tube, with the two wall curvature gauges 22 and 23 oriented in acommon, horizontal plane, as shown in FIG. 1. The tips of the probes 31,31 engage a pair of initial test points on the inner wall 27 of thetube, the test points lying in a common, radial plane. The compoundgauge is now advanced and/or retracted axially along the interior of thetube 11, e.g., by application of forces through a push-pull rod 41 (FIG.3).

Electric voltage signals are provided by the LVDTs 32,32, associatedwith the two diametrically opposed wall curvature gauges 22 and 23, insimilar manner to the operation of the LVDT 32 of the gauge 37, as thecompound gauge 12 is displaced axially through the tube. The outputsignal provided by each LVDT 32 is independent of that provided by theother LVDT, due to the substantially independent mounting of the gauges22 and 23 on the springs 24 and 26. The difference between the voltagesof the two LVDT signals constitutes an indication of the pattern ofaxial curvature along the length of the tube in the horizontal plane.

Two signal conditioners 42,42, (FIG. 3) are coupled to the LVDT's 32,32such that each signal conditioner receives the output signal from adifferent one of the LVDT's. The signal conditioners function to convertmodulated, alternating current voltage signals from the LVDT's intodirect current voltage signals which are proportional to thedisplacement of the probes 31,31 and which can be readily processed. Asseen in FIG. 3, the outputs of the signal conditioners are coupledtogether differentially so as to provide a single, continuous electricaloutput signal at 43, corresponding to the difference in voltages of thesignals from the two LVDTs 32,32, as the compound gauge 12 is advancedalong the tube 11.

The voltage pattern provided by the single output signal at 43constitutes a direct measure of the pattern along the tube of an axialcurvature component in the horizontal plane of the probes 31,31. This isdue to the fact that the voltage pattern follows the pattern ofinstantaneous differences between the voltage outputs from the twoLVDT's 32,32 as the compound gauge 12 is displaced along the length ofthe tube, i.e., the pattern of differences in the wall curvatures alongpairs of test points on diametrically opposite surfaces of the innerwall 27 of the tube. As previously explained with reference to FIGS. 5and 6, the difference in wall curvature gauge readings along thediametrically opposed wall surfaces of a tube, the surfaces lying in ahorizontal plane through the tube, is directly proportional to thecomponent of axial curvature in the horizontal plane.

A rotation of the tube about its axis, so as to bring additional axialplanes into a horizontal position, permits the taking of additionalreadings by the compound gauge 12. A plot of variations in the voltageof the signal axially of the tube, e.g., with traces taken for two axialplanes through the tube, provides an easily analyzed, completeindication of the axial curvature pattern. Such typical characteristicsas the root mean square value, maxima, minima and the periodic contentof the axial curvature may either be read directly from the plot ordetermined with a minimum of effort.

It must be emphasized that the simplified, direct, real time plot ofaxial curvature along the tube can be obtained only by a simultaneouspassing of the two wall curvature gauges through the tube alongdiametrically opposite tube wall surfaces, with the gauges mountedsubstantially independently of one another to eliminate any possibilityof interdependent readings, while a continuous electrical signalrepresenting wall curvature is generated by each of the gauges and whilethe two signals are combined so as to generate continuously a singleoutput signal having a voltage proportional to the difference betweentwo signals and, thus, to the magnitude of the axial curvature componentin plane. Thus, the rapidity of data taking and analysis is enhancedboth by the simultaneous obtaining of two wall curvature readings and bythe instantaneous and automatic processing of the two wall curvaturereadings into meaningful information concerning axial curvature alongthe tube.

The discussion thus far assumes an absence of any effects from higherorder, odd-foil distortions. An oddfoil distortion is a symmetricaldistortion characterized by an odd number of lobes in a tube crosssection, e.g., a trifoil distortion characterized by three lobes arrayedequiangularly about the axis of the tube. Axial offset or axialcurvature may be understood as a first order oddfoil distortion in that,if the effect is observed, without interruption, throughout a 360 scanabout the periphery of the inner wall of the tube, one cycle ofcurvature variation will be observed. For higher order odd foils,multiple cycles may be observed, if measurable.

It should be noted that even-foil distortions of any order and diametervariations will not affect the operation of the compound gauge 12.Even-foil distortions will be balanced out by a subtraction of values ofA r taken along opposed wall surfaces of the tube, as in the manneralready demonstrated for diameter variations.

Periodic odd-foil distortions, when viewed radially from the tube axis,may appear initially to constitute deviations in axial curvature. Uponfurther observa tion, however, they will be found to be periodic aboutthe periphery of the tube. In some instances, these higher orderodd-foil distortions may be ignored, inasmuch as they are generally muchless pronounced than those caused by variations in axial curvature. Suchhigher order odd-foil distortions may, however, be significant in suchfields as millimeter waveguide transmission, or where cylinders of adesired odd-foil geometry, e.g., triangular or pentagonal, are involved.Techniques for measuring axial curvature in a tube, with 9 higher orderodd-foil effects eliminated, are available through the use of compoundgauges'of the type of the invention.

In similar manner to the use of the compound gauge device 12 employingtwo gauges to eliminate the effects on axial curvature examination ofeven-foil distortions, compound gauge devices employing an odd number ofgauges may be utilized to eliminate the effects of higher order odd-foildistortions from the axial curvature measurement. Each such compounddevice is identical to the compound gauge device 12 in all respectsother than the number of probe carrier bars mounted independently atequiangular spacings about the axis of the device. Any trifoildistortions may be eliminated from the axial curvature measurementthrough the use of a three gauge device, five-foil distortions by a fivegauge device, etc.

The manner of operation of a three gauge device to provide directreadings of an axial curvature component in a plane independent of anytrifoil distortion effects will now be briefly described. This operationis considered exemplary of the use of a multiple gauge device forexamining axial curvature without encountering higher order odd-foileffects.

Turning to FIG. 7, a figure similar to FIG. 6, it is observed once againthat axial curvature in a horizontal X-Z plane offsets a tube crosssection Q with respect to a reference cross section R at a differentaxial location. One of three equiangularly arrayed wall curvature gaugesis taken as located in the X-Z plane. This assumption, convenient forpurposes of analysis, does not affect the validity of the analysis solong as readings are taken in two mutually perpendicular planes.

Since any trifoil distortion effects are equal and in like radialdirection for all of the gauges, only axial curvature effects are notedwhen a weighted algebraic sum is determined for the voltages of theoutput signals provided by the three gauges. This weighted algebraicsum, determined in a manner next to be described, in directlyproportional to an axial curvature component in the X-Z plane.

As seen in FIG. 7, the radial direction of the displacement A F; sensedby the tip ofa probe 31" of the gauge located in the X-Z plane isopposite to the radial direction of the X-Z plane components of thedisplacements A r, and A F; sensed by the tips of probes 31",31" of theother two gauges. The X component of displacements sensed by-the lattertwo gauges are observed each to be one-half of the total displacementsensed A F; or A 7'}, since each of these two gauges is disposed at a 60angle to the X-Z plane, which passes midway between the two gauges.Thus, the weighted average sum for the three gauge compound device,i.e., the proportionality factor varying directly with the X-Z planecomponent of axial curvature, corresponds to the difference between thereading of the gauge located in the X-Z plane and one-half the sum ofthe readings of the two gauges. The curvature equation, which parallelsEquations (8), (9 a) and (9b) forthe two probe device 12, is

-p 77=1 a (A 2. 1/2A?. 1/2A 2-.)

where k is a fixed proportionaltiy factor; A H, A K, and

A F, are the respective radial displacements illustrated in FIG. 7; andrespective weighting factors of+l l/2,

and l/2 are used to determine the weighted algebraic sum shown inparentheses at the right side of Equation IO).

The use of the weighted algebraic sum just discussed parallels the useas a curvature component indicator of the difference between thereadings of the two gauges of the compound device 12 describedpreviously. This diiTerence between the readings of the two gaugesconstitutes a weighted algebraic sum-fonthe two gauge device. Lookingagain at Equations (9a) and (9b), the weighted algebraic sum k (A r2 A 7includes weighting factors of +1 and l for the respective radialdisplacements A7] and A F (FIG. 6). In similar manner, weightedalgebraic sum equations may be determined for five gauge devices, sevengauge devices, etc. A family of such compound gauge devices may beemployed to examine axial curvature in the absence of effects ofdistortions of various types which may be considered significant.

It is to be understood that the described compound gauges and methodsare simply illustrative of certain embodiments of the invention.Alternative compound gauge devices might utilize common rigid carriersto mount independently two or more wall curvature gauges alongdiametrically opposed exterior surfaces of each tube being tested, inorder to explore axial curvature with reference to an outer wall of thetube, rather than the inner wall. Moreover, where exterior surfaces areto be utilized, the elongated member to be tested need not be hollow,but may instead be in the form of a solid cylinder, right circular orotherwise. Many other modifications may be made in accordance with theprinciples of the invention.

What is claimed is:

1. In a method of measuring the axial curvature of an elongated member:

a. sensing the wall curvature simultaneously and independently at anumber of test points on a wall surface of the elongated member, thetest points being arrayed equiangularly about the axis of the elongatedmember in a common, radially extending plane; while b. indicating aplanar component of the axial curvature of the elongated member at thetest points as a weighted algebraic sum of the individual wall curvaturevalues sensed at the test points.

2. In the method of claim 1, said step (b) comprising:

generating an electrical signal having a voltage pro portional to saidweighted algebraic sum of the individual wall curvature values sensed atthe test points.

3. In the method of claim 1, said steps (a) and (b) respectivelycomprising:

sensing the wall curvature at two test points at diametrically opposedpositions on the wall surface of the elongated member; and

indicating the differences between the individual wall curvature valuessensed at the two test points, said difference being proprotional to acomponent of the axial curvature of the elongated member, at the testpoints, in an axial plane which includes the test points.

4. In the method of claim 1, the elongated member being a tube and saidwall surface being an inner wall of the tube.

5. In a method of measuring the axial curvature of an elongated member,the steps of:

a. sensing the wall curvature independently at a number of initial testpoints on a wall surface of the elongated member, the initial testpoints being located in a common, radially extending test planeintersecting the axis of the elongated member perpendicularly, theinitial test points being arrayed equiangularly about the axis of theelongated member; while b. indicating a planar component of the axialcurvature of the elongated member at said initial test points as aweighted algebraic sum of the individual wall curvature values sensed atthe test points; and then 0. repeating steps (a) and (b) for a pluralityof further radially extending test planes intersecting the axis of theelongated member perpendicularly at at least several further positionsalong the axis, the number of additional test points on the wall surfaceof the elongated member being examined in each of said further radiallyextending test planes corresponding to said number of initial testpoints, the additional test points and the initial test pointsdescribing a number of equiangularly arrayed, axially extending lines onthe wall surface of the elongated member, the number of said linescorresponding to said number of initial test points.

6. In the method of claim 5, said step (b) comprising:

generating an electrical signal having a voltage proportional to saidweighted algebraic sum of the individual wall curvatures sensed at theinitial test points.

7. In the method of claim 5, the elongated member being a tube, saidstep (a) comprising:

sensing the wall curvature at a number of initial test points situatedon an inner wall of the tube.

8. In the method of claim 5, said step (a) comprisingz sensing the wallcurvature at two initial test points at diametrically opposed positionson the wall surface of the elongated member. 9. In the method of claim8, said step (b) comprising: indicating the difference between theindividual wall curvature values sensed at the two initial test points,said difference being proportional to a component of the axial curvatureof the elongated member, at the initial test points, in an axial planewhich includes the initial test points. 10. In the method of claim 5,said step (a) comprissensing the wall curvature at three initial testpoints arrayed equiangularly about the axis of the elongated member. II.In the method of claim 10, said step (b) comprismg:

indicating the difference between the individual wall curvature valuesensed at one of the initial test points and one half the sum of theindividual wall curvature values sensed at the other two initial testpoints, said difference being proportional to a component of the axialcurvature of the elongated member, at the initial test points, in anaxial plane which includes said one initial test point and passes midwaybetween said other two initial test points. 12. In a method of measuringthe axial curvature of an elongated member, the steps of:

a. sensing the wall curvature at a first test point on a wall surface ofthe elongated member; while simultaneously b. sensing the wall curvatureat a second test point on the wall surface of the elongated member, thesecond test point lying diametrically opposite the first test point,sensing steps (a) and (b) being independent of one another; and while c.indicating the difference in wall curvature values sensed for the firstand second test points, said difference corresponding to a component ofthe axial curvature of the elongated member, at said first and secondtest points, in an axial plane which includes the first and second testpoints; and then d. repeating steps (a) through (c) at a plurality ofadditional locations along the length of the elongated memberconstituting, with the first and second test points, a succession offirst test points lying along a first axially extending path and asuccession of second test points lying along a second, diametricallyopposed, axially extending path, thereby indieating an axial pattern ofsaid difierence along the first and second axially extending pathsv 13.In the method of claim 12, said step (c) comprismg:

generating an electrical signal having a voltage proportional to saiddifference in sensed wall curvature values.

14. In the method of claim 12, the elongated member being a tube, saidsensing steps (a) and (b) each comprising:

sensing the wall curvature at a test point situated on an inner wall ofthe tube.

15. In the method of claim 12:

repeating steps (a) through (d) in at least one additional, axiallyextending test plane differing from an axially extending test planedefined by said first and second axially extending paths.

16. In the method of claim 15, said axially extending test planes beingtwo, mutually perpendicular, axially extending test planes.

17. In a method of measuring the axial curvature of an elongated member,the steps of:

a. sensing the radial displacement of a first test point, situated on awall surface of the elongated member, relative to a first axiallyextendng reference line joining two reference points on said wallsurface spaced at known distances from said first test point at axiallyopposite sides of the first test point; while simultaneously b. sensingthe radial displacement of a second test point, situated diametricallyopposite said first test point on the wall surface of the elongatedmember, relative to a second axially extending reference line joiningtwo additional reference points on the wall surface spaced atcorresponding known distances from said second test point at axiallyopposite sides of the second test point, sensing steps (a) and (b) beingindependent of one another; and while c. generating an electrical signalhaving a voltage proportional to the difference in radial displacementssensed for said first and second test points so as to indicate themagnitude of said difference; and then d. repeating steps (a) through(c) at a plurality of additional locations along the length of theelongated member constituting, with said first and second test points, asuccession of first test points lying along a first axially extendingpath and a succession of second test points lying along a second,diametrically opposed, axially extending path, thereby indicating anaxial pattern of said difierence along said first and second axiallyextending paths. 18. In the method of claim 17, the elongated memberbeing a tube, said sensing steps each comprising:

sensing the relative radial position of a test point situated on theinner wall of the tube. 19. In a device for measuring the axialcurvature of a elongated member:

a carrier; a number of means, supported by the carrier, for each,independently of the other means, sensing the wall curvature at adifferent one of a corresponding number of test points on a wall surfaceof the elongated member, the test points lying in a common, radiallyextending test plane perpendicularly intersecting the axis of theelongated member and being arrayed equiangularly about the axis of theelongated member;

means for indicating a planar component of the axial curvature of theelongated member at said test points as a weighted algebraic sum of theindividual wall curvature values sensed by the independent wallcurvature sensing means; and

means for moving the carrier axially along the elongated member.

20. In the device of claim 19, said indicating means comprising:

means for generating an electrical signal having a voltage proportionalto said weighted algebraic sum of the individual wall curvature sensedby the independent sensing means.

21. In the device of claim 19, wherein the elongated member is a tubeand wherein said wall surface constitutes the inner wall of the tube,said carrier moving means comprising:

means for advancing the carrier and the independent sensing meansaxially along the interior of the tube.

22. In the device of claim 19, said number of sensing means being two,the two sensing means being so positioned on the carrier as to sense thewall curvature at two test points at diametrically opposite locations onthe wall surface of the elongated member.

23. In the device of claim 22, said indicating means comprising:

means for indicating the difference between the individual wallcurvature values sensed by the two sensing means, said difference beingproportional to a component of the axial curvature of the elongatedmember, at the test points, in an axial plane which includes the testpoints.

24. In the device of claim 19, said number of sensing means being three,the three sensing means being so positioned on the carrier as to sensethe wall curvature at three test points arrayed equiangularly about theaxis of the elongated member.

25. In the device of claim 24, said indicating means comprising:

means for indicating the difference between the wall curvature valuesensed by the sensing means at one of the three test points and one halfthe sum of the individual wall curvatures sensed by the two sensingmeans at the other two test points, said difference being proportionalto a component of the axial curvature of the elongated member, at thetest points, in an axial plane which includes said one test point andpasses midway between said other two test points. 26. In a device formeasuring the axial curvature of an elongated member:

a carrier; first means, supported by the carrier, for sensing the wallcurvature at a first test point on a wall surface of the elongatedmember; second means, supported by the carrier independently of thefirst sensing means, for sensing the wall curvature at a second point onthe wall surface of the elongated member lying diametrically oppositethe first test point; means for indicating the difference in wallcurvatures sensed by the first and second sensing means, said differencecorresponding to a component of the axial curvature of the elongatedmember, at said first and second test points, in an axial plane whichincludes the first and second test points; and means for moving thecarrier axially along the elongated member. 27. In the device of claim26, said indicating means comprising:

means for generating an electrical signal having a voltage proportionalto said difference in sensed wall curvature values. 28."In the device ofclaim 26, wherein the elongated member is a tube and wherein said wallsurface constitutes the inner wall surface of the tube, said carriermoving means comprising:

means for advancing the carrier and the first and second sensing meansaxially along the interior of .the tube.

29. In a device for measuring the axial curvature of an elongatedmember:

a carrier;

first probe means, supported by the carrier, for sensing the radialdisplacement of a first test point, situated on a wall surface of theelongated member, relative to a first axially extending reference linejoining two reference points on the wall surface spaced at knowndistances from said first test point i at axially opposite sides of thefirst test point;

l second probe means, supported by the carrier independently of saidfirst probe means, for sensing the radial displacement of a second testpoint, situated diametrically opposite said first test point on the wallsurface of the elongated member, relative to a second axially extendingreference line joining two additional reference points on the wallsurface spaced at corresponding known distances from said second testpoint at axially opposite sides of the second test point;

means for indicating the difference in radial displacements sensed bythe first and second probe means; and means for moving the carrieraxially along the elongated member. 30. In the device of claim 29, saidindicating means comprising:

means for generating an electrical signal having a voltage proportionalto the difference in radial displacements sensed by the first and secondprobe means. 31. In the device of claim 29, wherein the elongated memberis a tube and wherein said wall surface constitutes the inner wallsurface of the tube, said carrier moving means comprising:

means for advancing the carrier and the first and second probe meansaxially along the interior of the tube.

32. In the device of claim 31, the carrier comprising:

biasing means for urging each of said first and second probe meansradially outward toward the inner wall surface of the tube.

33. In the device of claim 31, the carrier comprising:

a first subcarrier mounting said first probe means,

a second subcarrier supported substantially independently from saidfirst subcarrier and mounting said second probe means, and

means for biasing the first and second subcarriers diametrically apart.

34. In the device of claim 33, the carrier comprising:

a pair of first feet projecting radially outwardly from the firstsubcarrier, the first feet positioned such that, due to the effect ofsaid biasing means on the first subcarrier, a radially outermost tip ofeach first foot contacts a different one of said reference points on thefirst axially extending reference line; and

a pair of second feet projecting radially outwardly from the secondsubcarrier, the second feet positioned such that, due to the urging ofsaid biasing means on the second subcarrier, a radially outermost tip ofeach second foot contacts a different one of said additional referencepoints on the second axially extending reference line.

35. A device for measuring the axial curvature of a tube, which devicecomprises:

a carrier frame having a longitudinal axis;

a plurality of radially projecting means, comprising two sets ofspring-loaded plungers, the plungers of each set being equiangularlyarrayed about an axis of the carrier frame with one set adjacent to eachend of the carrier frame, for supporting the carrier frame within thetube coaxially with the tube;

first and second axially extending bars mounted independently of oneanother in diametrically opposed positions on the carrier frame;

means supported by the carrier frame for biasing said bars diametricallyapart;

a pair of radially extending feet on each bar. one foot of each pairpositioned adjacent to each axial end of the associated bar, forcontacting adjacent reference points on an inner wall of the tube, thecontacted reference points defining first and second reference linesadjacent to said first and second bars, respectively;

a pair of probes, one on each bar, each probe located in a fixedlongitudinal position between the feet on its respective bar;

means for biasing each of the probes radially outwardly so as each toengage an adjacent test point at one of two diametrically opposedlocations on the inner wall of the tube;

means for displacing the carrier frame, and with it the bars and theprobes, axially through the tube; and

means for generating an electrical signal having a voltage proportionalto the instantaneous difference in the radial displacements of the firstand second probes relative to said first and second diametricallyopposed reference lines, respectively.

UNITED STATES, PATENT OFFICE CERTIFICATE OF CORRECTION PatentNo.3,780,442 pm e r 25, 1973 ltis certified that error appears in theabove-identified patent and that said Letters Patent are herebycorrected as shown below:

In the specification, Column 1, line 9, "data." should read --date--;lines 25-26, "minimal," should read --minimal.--; line 34, "secon"should read --section--. Column 6, lines 53-5 the equation should be setout on one line and numbered --(7)- Column 9, line 39, "described, in"should read --described," i-s'--.

. In the claims, Column 10, line 59, 'prop rotional" should read--proportional--.

Signed-and sealed this 30th day of July 197 (SEAL) Attest':

c. MARSHALL DANN Commissioner of Patents MCCOY M. GIBSON, JR. AttestingOfficer

1. In a method of measuring the axial curvature of an elongated member:a. sensing the wall curvature simultaneously and independently at anumber of test points on a wall surface of the elongated member, thetest points being arrayed equiangularly about the axis of the elongatedmember in a common, radially extending plane; while b. indicating aplanar component of the axial curvature of the elongated member at thetest points as a weighted algebraic sum of the individual wall curvaturevalues sensed at the test points.
 2. In the method of claim 1, said step(b) comprising: generating an electrical signal having a voltageproportional to said weighted algebraic sum of the individual wallcurvature values sensed at the test points.
 3. In the method of claim 1,said steps (a) and (b) respectively comprising: sensing the wallcurvature at two test points at diametrically opposed positions on thewall surface of the elongated member; and indicating the differencesbetween the individual wall curvature values sensed at the two testpoints, said difference being proprotional to a component of the axialcurvature of the elongated member, at the test points, in an axial planewhich includes the test points.
 4. In the method of claim 1, theelongated member being a tube and said wall surface being an inner wallof the tube.
 5. In a method of measuring the axial curvAture of anelongated member, the steps of: a. sensing the wall curvatureindependently at a number of initial test points on a wall surface ofthe elongated member, the initial test points being located in a common,radially extending test plane intersecting the axis of the elongatedmember perpendicularly, the initial test points being arrayedequiangularly about the axis of the elongated member; while b.indicating a planar component of the axial curvature of the elongatedmember at said initial test points as a weighted algebraic sum of theindividual wall curvature values sensed at the test points; and then c.repeating steps (a) and (b) for a plurality of further radiallyextending test planes intersecting the axis of the elongated memberperpendicularly at at least several further positions along the axis,the number of additional test points on the wall surface of theelongated member being examined in each of said further radiallyextending test planes corresponding to said number of initial testpoints, the additional test points and the initial test pointsdescribing a number of equiangularly arrayed, axially extending lines onthe wall surface of the elongated member, the number of said linescorresponding to said number of initial test points.
 6. In the method ofclaim 5, said step (b) comprising: generating an electrical signalhaving a voltage proportional to said weighted algebraic sum of theindividual wall curvatures sensed at the initial test points.
 7. In themethod of claim 5, the elongated member being a tube, said step (a)comprising: sensing the wall curvature at a number of initial testpoints situated on an inner wall of the tube.
 8. In the method of claim5, said step (a) comprising: sensing the wall curvature at two initialtest points at diametrically opposed positions on the wall surface ofthe elongated member.
 9. In the method of claim 8, said step (b)comprising: indicating the difference between the individual wallcurvature values sensed at the two initial test points, said differencebeing proportional to a component of the axial curvature of theelongated member, at the initial test points, in an axial plane whichincludes the initial test points.
 10. In the method of claim 5, saidstep (a) comprising: sensing the wall curvature at three initial testpoints arrayed equiangularly about the axis of the elongated member. 11.In the method of claim 10, said step (b) comprising: indicating thedifference between the individual wall curvature value sensed at one ofthe initial test points and one half the sum of the individual wallcurvature values sensed at the other two initial test points, saiddifference being proportional to a component of the axial curvature ofthe elongated member, at the initial test points, in an axial planewhich includes said one initial test point and passes midway betweensaid other two initial test points.
 12. In a method of measuring theaxial curvature of an elongated member, the steps of: a. sensing thewall curvature at a first test point on a wall surface of the elongatedmember; while simultaneously b. sensing the wall curvature at a secondtest point on the wall surface of the elongated member, the second testpoint lying diametrically opposite the first test point, sensing steps(a) and (b) being independent of one another; and while c. indicatingthe difference in wall curvature values sensed for the first and secondtest points, said difference corresponding to a component of the axialcurvature of the elongated member, at said first and second test points,in an axial plane which includes the first and second test points; andthen d. repeating steps (a) through (c) at a plurality of additionallocations along the length of the elongated member constituting, withthe first and second test points, a succession of first test pointslying along a first axially extending path and a succession of secondtest points lying aloNg a second, diametrically opposed, axiallyextending path, thereby indicating an axial pattern of said differencealong the first and second axially extending paths.
 13. In the method ofclaim 12, said step (c) comprising: generating an electrical signalhaving a voltage proportional to said difference in sensed wallcurvature values.
 14. In the method of claim 12, the elongated memberbeing a tube, said sensing steps (a) and (b) each comprising: sensingthe wall curvature at a test point situated on an inner wall of thetube.
 15. In the method of claim 12: repeating steps (a) through (d) inat least one additional, axially extending test plane differing from anaxially extending test plane defined by said first and second axiallyextending paths.
 16. In the method of claim 15, said axially extendingtest planes being two, mutually perpendicular, axially extending testplanes.
 17. In a method of measuring the axial curvature of an elongatedmember, the steps of: a. sensing the radial displacement of a first testpoint, situated on a wall surface of the elongated member, relative to afirst axially extendng reference line joining two reference points onsaid wall surface spaced at known distances from said first test pointat axially opposite sides of the first test point; while simultaneouslyb. sensing the radial displacement of a second test point, situateddiametrically opposite said first test point on the wall surface of theelongated member, relative to a second axially extending reference linejoining two additional reference points on the wall surface spaced atcorresponding known distances from said second test point at axiallyopposite sides of the second test point, sensing steps (a) and (b) beingindependent of one another; and while c. generating an electrical signalhaving a voltage proportional to the difference in radial displacementssensed for said first and second test points so as to indicate themagnitude of said difference; and then d. repeating steps (a) through(c) at a plurality of additional locations along the length of theelongated member constituting, with said first and second test points, asuccession of first test points lying along a first axially extendingpath and a succession of second test points lying along a second,diametrically opposed, axially extending path, thereby indicating anaxial pattern of said difference along said first and second axiallyextending paths.
 18. In the method of claim 17, the elongated memberbeing a tube, said sensing steps each comprising: sensing the relativeradial position of a test point situated on the inner wall of the tube.19. In a device for measuring the axial curvature of a elongated member:a carrier; a number of means, supported by the carrier, for each,independently of the other means, sensing the wall curvature at adifferent one of a corresponding number of test points on a wall surfaceof the elongated member, the test points lying in a common, radiallyextending test plane perpendicularly intersecting the axis of theelongated member and being arrayed equiangularly about the axis of theelongated member; means for indicating a planar component of the axialcurvature of the elongated member at said test points as a weightedalgebraic sum of the individual wall curvature values sensed by theindependent wall curvature sensing means; and means for moving thecarrier axially along the elongated member.
 20. In the device of claim19, said indicating means comprising: means for generating an electricalsignal having a voltage proportional to said weighted algebraic sum ofthe individual wall curvature sensed by the independent sensing means.21. In the device of claim 19, wherein the elongated member is a tubeand wherein said wall surface constitutes the inner wall of the tube,said carrier moving means comprising: means for advancing the carrierand the independent sensing means axially alOng the interior of thetube.
 22. In the device of claim 19, said number of sensing means beingtwo, the two sensing means being so positioned on the carrier as tosense the wall curvature at two test points at diametrically oppositelocations on the wall surface of the elongated member.
 23. In the deviceof claim 22, said indicating means comprising: means for indicating thedifference between the individual wall curvature values sensed by thetwo sensing means, said difference being proportional to a component ofthe axial curvature of the elongated member, at the test points, in anaxial plane which includes the test points.
 24. In the device of claim19, said number of sensing means being three, the three sensing meansbeing so positioned on the carrier as to sense the wall curvature atthree test points arrayed equiangularly about the axis of the elongatedmember.
 25. In the device of claim 24, said indicating means comprising:means for indicating the difference between the wall curvature valuesensed by the sensing means at one of the three test points and one halfthe sum of the individual wall curvatures sensed by the two sensingmeans at the other two test points, said difference being proportionalto a component of the axial curvature of the elongated member, at thetest points, in an axial plane which includes said one test point andpasses midway between said other two test points.
 26. In a device formeasuring the axial curvature of an elongated member: a carrier; firstmeans, supported by the carrier, for sensing the wall curvature at afirst test point on a wall surface of the elongated member; secondmeans, supported by the carrier independently of the first sensingmeans, for sensing the wall curvature at a second point on the wallsurface of the elongated member lying diametrically opposite the firsttest point; means for indicating the difference in wall curvaturessensed by the first and second sensing means, said differencecorresponding to a component of the axial curvature of the elongatedmember, at said first and second test points, in an axial plane whichincludes the first and second test points; and means for moving thecarrier axially along the elongated member.
 27. In the device of claim26, said indicating means comprising: means for generating an electricalsignal having a voltage proportional to said difference in sensed wallcurvature values.
 28. In the device of claim 26, wherein the elongatedmember is a tube and wherein said wall surface constitutes the innerwall surface of the tube, said carrier moving means comprising: meansfor advancing the carrier and the first and second sensing means axiallyalong the interior of the tube.
 29. In a device for measuring the axialcurvature of an elongated member: a carrier; first probe means,supported by the carrier, for sensing the radial displacement of a firsttest point, situated on a wall surface of the elongated member, relativeto a first axially extending reference line joining two reference pointson the wall surface spaced at known distances from said first test pointat axially opposite sides of the first test point; second probe means,supported by the carrier independently of said first probe means, forsensing the radial displacement of a second test point, situateddiametrically opposite said first test point on the wall surface of theelongated member, relative to a second axially extending reference linejoining two additional reference points on the wall surface spaced atcorresponding known distances from said second test point at axiallyopposite sides of the second test point; means for indicating thedifference in radial displacements sensed by the first and second probemeans; and means for moving the carrier axially along the elongatedmember.
 30. In the device of claim 29, said indicating means comprising:means for generating an electrical signal having a voltage proportIonalto the difference in radial displacements sensed by the first and secondprobe means.
 31. In the device of claim 29, wherein the elongated memberis a tube and wherein said wall surface constitutes the inner wallsurface of the tube, said carrier moving means comprising: means foradvancing the carrier and the first and second probe means axially alongthe interior of the tube.
 32. In the device of claim 31, the carriercomprising: biasing means for urging each of said first and second probemeans radially outward toward the inner wall surface of the tube.
 33. Inthe device of claim 31, the carrier comprising: a first subcarriermounting said first probe means, a second subcarrier supportedsubstantially independently from said first subcarrier and mounting saidsecond probe means, and means for biasing the first and secondsubcarriers diametrically apart.
 34. In the device of claim 33, thecarrier comprising: a pair of first feet projecting radially outwardlyfrom the first subcarrier, the first feet positioned such that, due tothe effect of said biasing means on the first subcarrier, a radiallyoutermost tip of each first foot contacts a different one of saidreference points on the first axially extending reference line; and apair of second feet projecting radially outwardly from the secondsubcarrier, the second feet positioned such that, due to the urging ofsaid biasing means on the second subcarrier, a radially outermost tip ofeach second foot contacts a different one of said additional referencepoints on the second axially extending reference line.
 35. A device formeasuring the axial curvature of a tube, which device comprises: acarrier frame having a longitudinal axis; a plurality of radiallyprojecting means, comprising two sets of spring-loaded plungers, theplungers of each set being equiangularly arrayed about an axis of thecarrier frame with one set adjacent to each end of the carrier frame,for supporting the carrier frame within the tube coaxially with thetube; first and second axially extending bars mounted independently ofone another in diametrically opposed positions on the carrier frame;means supported by the carrier frame for biasing said bars diametricallyapart; a pair of radially extending feet on each bar, one foot of eachpair positioned adjacent to each axial end of the associated bar, forcontacting adjacent reference points on an inner wall of the tube, thecontacted reference points defining first and second reference linesadjacent to said first and second bars, respectively; a pair of probes,one on each bar, each probe located in a fixed longitudinal positionbetween the feet on its respective bar; means for biasing each of theprobes radially outwardly so as each to engage an adjacent test point atone of two diametrically opposed locations on the inner wall of thetube; means for displacing the carrier frame, and with it the bars andthe probes, axially through the tube; and means for generating anelectrical signal having a voltage proportional to the instantaneousdifference in the radial displacements of the first and second probesrelative to said first and second diametrically opposed reference lines,respectively.